I learned multiplication long before computers were commonplace, and when four-banger calculators were still quite expensive. The reason I can't do that calculation in my head (well, I could but it would be faster to grab a pen) is that I don't have enough stable registers. I'd guess maybe two registers that won't get corrupted during the calculation. They're not big registers, either.

Regardless, I'm not saying that there isn't a technique that would allow me to improve. I'm saying my inability has nothing to do with ubiquitous electronics.